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Brillouin zone

About: Brillouin zone is a research topic. Over the lifetime, 13849 publications have been published within this topic receiving 383077 citations.


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Journal ArticleDOI
TL;DR: The density-functional linear-response approach to lattice-dynamical calculations in semiconductors is presented in full detail and real-space interatomic force constants for these materials are obtained, which are useful both for interpolating the dynamical matrices through the Brillouin zone, and as ingredients of approximate calculations for mixed systems such as alloys and microstructures.
Abstract: The density-functional linear-response approach to lattice-dynamical calculations in semiconductors is presented in full detail. As an application, we calculate complete phonon dispersions for the elemental semiconductors Si and Ge, and for the III-V semiconductor compounds GaAs, AlAs, GaSb, and AlSb. Our results are in excellent agreement with experiments where available, and provide predictions where they are not. As a byproduct, we obtain real-space interatomic force constants for these materials, which are useful both for interpolating the dynamical matrices through the Brillouin zone, and as ingredients of approximate calculations for mixed systems such as alloys and microstructures. The possibility of studying these systems using the force constants of the pure materials relies on the so-called mass approximation, B i.e., on neglecting the dependence of the force constants upon composition. The accuracy of such an approximation is tested and found to be very good for cationic intermixing in binary semiconductors, while it is less so for anionic substitutions. The situation is intermediate in the case of elemental semiconductors.

1,301 citations

Journal ArticleDOI
TL;DR: In this paper, a perturbation calculation which starts with wave functions of the two-dimensional lattice and is applied to the three-dimensional graphite lattice is described and general features of the structure of the $\ensuremath{\pi}$ bands in the neighborhood of the zone edge are obtained and are expressed in terms of appropriate parameters.
Abstract: Tight-binding calculations, using a two-dimensional model of the graphite lattice, lead to a point of contact of valence and conduction bands at the corner of the reduced Brillouin zone. A perturbation calculation which starts with wave functions of the two-dimensional lattice and is applied to the three-dimensional lattice is described. Some general features of the structure of the $\ensuremath{\pi}$ bands in the neighborhood of the zone edge are obtained and are expressed in terms of appropriate parameters.

1,269 citations

Journal ArticleDOI
TL;DR: In this article, the authors show that a family of nonmagnetic materials including TaAs, TaP, NbAs and NbP are Weyl semimetal (WSM) without inversion center.
Abstract: Based on first principle calculations, we show that a family of nonmagnetic materials including TaAs, TaP, NbAs and NbP are Weyl semimetal (WSM) without inversion center. We find twelve pairs of Weyl points in the whole Brillouin zone (BZ) for each of them. In the absence of spin-orbit coupling (SOC), band inversions in mirror invariant planes lead to gapless nodal rings in the energy-momentum dispersion. The strong SOC in these materials then opens full gaps in the mirror planes, generating nonzero mirror Chern numbers and Weyl points off the mirror planes. The resulting surface state Fermi arc structures on both (001) and (100) surfaces are also obtained and show interesting shapes, pointing to fascinating playgrounds for future experimental studies.

1,266 citations

Book
01 Jan 1963
TL;DR: In this article, the Hartree-Fock Approximation of many-body techniques and the Electron Gas Polarons and Electron-phonon Interaction are discussed.
Abstract: Mathematical Introduction Acoustic Phonons Plasmons, Optical Phonons, and Polarization Waves Magnons Fermion Fields and the Hartree-Fock Approximation Many-body Techniques and the Electron Gas Polarons and the Electron-phonon Interaction Superconductivity Bloch Functions - General Properties Brillouin Zones and Crystal Symmetry Dynamics of Electrons in a Magnetic Field: de Haas-van Alphen Effect and Cyclotron Resonance Magnetoresistance Calculation of Energy Bands and Fermi Surfaces Semiconductor Crystals I: Energy Bands, Cyclotron Resonance, and Impurity States Semiconductor Crystals II: Optical Absorption and Excitons Electrodynamics of Metals Acoustic Attenuation in Metals Theory of Alloys Correlation Functions and Neutron Diffraction by Crystals Recoilless Emission Green's Functions - Application to Solid State Physics Appendix: Perturbation Theory and the Electron Gas Index.

1,132 citations

Journal ArticleDOI
TL;DR: The relation between two different interpretations of the Hall conductance as topological invariants is clarified and it is found that vortices are given by the edge states when they are degenerate with the bulk states.
Abstract: We consider the integer quantum Hall effect on a square lattice in a uniform rational magnetic field. The relation between two different interpretations of the Hall conductance as topological invariants is clarified. One is the Thouless--Kohmoto--Nightingale--den Nijs (TKNN) integer in the infinite system and the other is a winding number of the edge state. In the TKNN form of the Hall conductance, a phase of the Bloch wave function defines U(1) vortices on the magnetic Brillouin zone and the total vorticity gives ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{y}}$. We find that these vortices are given by the edge states when they are degenerate with the bulk states.

1,118 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023430
2022957
2021463
2020543
2019568
2018587